You can argue that there are pro’s but also cons. Don’t get me wrong, DSP processing of audio is fabulously flexible, and I rely on it for my living room in both Roon and to EQ my sub.
The main argument against a DSP crossover really is the quality of the ADC/DAC combination. You buy a nice Berkeley, Mytek or whatever brand DAC, and you feed.... dsp based speakers? To me that makes no sense as the DSP must:
1 - Convert the analog to digital using an ADC
2 - Process it
3 - Convert the digital into analog
Now, if you can do this all in the digital domain before the signal hits the system, like with say a digital preamp, or Roon, then no problem.
An active/analog XO still has potential drawbacks, including the quality of the components and the additional analog stages that must be put in line, which will introduce flavors, distortion and noise of their own.
In either case, you’ll need more amps.
With a passive, speaker level crossover you ALSO introduce a number of issues, like reduced efficiency (due to voltage square vs. power) and the need to spend WAY too much to get great components, but you only buy a stereo amp for 2 speakers. :)
This is why to me, at the end of the day the whole package/end result is what matters most. I have to say though that the idea of having say, a digital pre amp that feeds the speakers a digital signal, and no additional amps is pretty damn sweet sounding. :) Meridian sure was ahead of their time here.